Method for determining downhole pressure

ABSTRACT

A pressure in a wellbore and a temperature at least at one point of the wellbore are measured during wellbore testing. Transient profiles of temperature along the wellbore are determined and changes in a density of a downhole fluid and in a length of atubing when the wellbore is shut in are calculated. The pressure measurement results are corrected on the basis of the calculated changes in the density of the downhole fluid and in the length of the tubing.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to Russian Application No. 2014135163filed Aug. 28, 2014, which is incorporated herein by reference in itsentirety.

BACKGROUND

The disclosure relates to the field of studying oil and gas wells and isdesigned to correct results of pressure measurements in high-rate wells,performed during well tests.

At present, significant improvement in the accuracy and reliability ofpressure sensors takes place. The pressure sensors have a resolutionbetter than 0.01 psi and an absolute measurement accuracy of the orderof 1 psi. This is especially significant in study of high-productiveformations when rapid increase in a pressure is followed by very slowincrease in the pressure for a long time. In this case, temperaturevariations which occur during a well test can change even the nature ofpressure variation during the second—slow—stage: the pressure candecrease and not increase in a shut-in well.

Investigation of oil/gas formation properties by analyzing dynamics ofpressure variation in a well at a change in the productivity of the well(including said change when the well is shut in) is called as PressureTransient Analysis (PTA). The traditional techniques for processing dataobtained in the PTA do not take into account a possible influence ofnon-isothermal effects and assume that a pressure sensor is at a fixeddistance (50 to 100 m) from an upper boundary of a formation to bestudied. Modern techniques for processing the PTA data (cf., Kuchuk F.J., Onur M., Hollaender F. Monograph series: Vol. 57. Pressure TransientFormation and Well Testing (1st ed.). ELSEVIER, 2010, pp. xv-xx, 23-26)comprise stimulating an inflow of a fluid from a formation, taking asample and registering a flow rate and a pressure, preferably a bottomhole pressure. The PTA data is currently interpreted using analyticalsolutions of the piezoconductivity equation at various well completionschemes and various boundary conditions. The developed analyticaltechniques are applicable to fractured, layered, horizontally andradially composite formations. Numerical simulation techniques are usedfor even more complicated heterogeneous systems and multiphase flows. Inthe majority of cases, however, all analytical and numerical methodsassume the flow of a fluid under isothermal conditions. With this,reduction in a pressure, as logged in some high-rate wells, shows thatthe traditional isothermal techniques for interpretation of measurementresults are not applicable in such wells.

SUMMARY

The technical result provided by the invention is an enhanced accuracyof downhole pressure measurement due to taking non-isothermal effectsinto account.

In accordance with the method, a pressure in a wellbore and atemperature at least at one point of the wellbore are measured duringwellbore testing. Then, transient profiles of temperature along thewellbore are determined during the wellbore testing and changes in adensity of a downhole fluid and in a length of a tubing when thewellbore is shut in are calculated. The pressure measurement results arecorrected on the basis of the calculated changes in the density of thedownhole fluid and in the length of the tubing.

The transient profiles of the temperature along the wellbore aredetermined by measuring the temperature along the wellbore using asystem of sensors distributed on the wellbore at different depths or bynumerical or analytical simulating the temperature profile. Ifnecessary, the continuous transient profiles of the temperature can beobtained by interpolating the measured temperatures.

The pressure is measured using at least one sensor disposed at a fixeddepth within the wellbore.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure is illustrated by the drawings wherein:

FIG. 1 shows a comparison of the bottom hole pressure recovery dynamicsduring the wellbore shut-in under isothermal and non-isothermalconditions;

FIG. 2 shows simulated downhole temperatures at a depth of a sensor andat a surface during the wellbore testing;

FIG. 3 shown a simulated downhole pressure at the depth of a sensor andat the surface during the wellbore testing;

FIG. 4 shows non-stationary profiles of the temperature along thewellbore for a wellbore shut-in mode used for processing the PTAresults;

FIG. 5 a shows change in an average temperature of a downhole fluidbetween a tubing anchorage point and a pressure sensor;

FIG. 5 b shows a density of the downhole fluid between the sensor and anupper boundary of a reservoir;

FIG. 5 c shows variation in a tubing length (the right graph) in timewhen the wellbore is shut in;

FIG. 6 shows a comparison of the bottom hole pressure recovery dynamicsin an oil formation after production without and with takingnon-isothermal effects into account.

DETAILED DESCRIPTION

A wellbore testing is divided into two periods: an inflow period and apressure recovery period. In the first period, the wellbore is opened tooperate at a constant or variable flow rate, wherein a downhole pressuredrops. For a time depending upon targets of the wellbore testing,formation properties, a bottom-hole zone state, reservoir fluidproperties, and a pressure draw-down, the wellbore is shut in, and thepressure is recovered up to its original value.

Pressure and temperature sensors are usually placed on a tubingapproximately at a distance L₀=100 M above an upper boundary of areservoir. Since a temperature of a fluid to be produced is essentiallyhigher than an average temperature of overlying rocks, heating of rocksnear the wellbore takes place. After shutting the wellbore in, atemperature in the vicinity of the borehole decreases, a fluid fillingthe wellbore is cooled down to a geothermal temperature, and an averagetemperature of said fluid decreases. Calculations show that the averagetemperature of the downhole fluid can decrease down to 30-40° C. in caseof deep wells (4,000-6,000 m).

This circumstance can result in effects as follows:

1) a density of the fluid filling the wellbore in an interval betweenthe pressure sensor and the reservoir increases;

2) a length of the tubing (anchored at the surface) changes and aposition of the sensor relative to the reservoir changes.

Both said effects leads to reduction in measured pressure.

A pressure change related to a downhole temperature change can becalculated by the formula (1):

ΔP(t)=g·[ ρ (t)·(L ₀ +ΔL(t))− ρ(0)·L ₀],  (1)

r

e ΔP(t) is a pressure change, Pa; ρ(t) is a downhole fluid density belowthe pressure sensor, kg/m³; ρ(0) is an average downhole fluid densitybelow the pressure sensor immediately after shutting the well in, kg/m³;L₀ is an initial position of the pressure sensor immediately aftershutting the wellbore in, m; ΔL(t) is a change in a tubing length (froma surface anchorage point to the sensor) in the shut-in well, m; g is agravity acceleration, m/s².

An increase of the fluid density below the pressure sensor is determinedby a volumetric thermal expansion coefficient of the fluid, α_(f), K⁻¹,and by a change in the average temperature of the fluid below the sensorin the shut-in well, ΔT(t), K:

ρ(t)= ρ(0)·(1−α_(f) ·ΔT(t)).  (2)

A decrease in the tubing length, ΔL(t), and respective change in thesensor position is determined by a linear thermal expansion coefficientof the tubing, α_(t), K⁻¹, and by a variation in a temperature profilethrough a depth (from an surface anchorage point to the sensor) in theshut-in well, m; g is a gravity acceleration, m/s². To determine thevalue ΔL(t), it is proposed to divide a distance between the tubinganchorage point and the pressure sensor into n equal sections andcalculate a reduction in the tubing length by the formula (3):

$\begin{matrix}{{{\Delta \; {L(t)}} = {{L_{0} \cdot \alpha_{t} \cdot \frac{1}{n}}{\sum\limits_{i = 1}^{n}( {T_{oi} - {T_{i}(t)}} )}}},} & (3)\end{matrix}$

r

e T_(i)(t) is a temperature of i^(th) section at a time

t (i=1, . . . n) in the shut-in well,

; T_(oi) a temperature of i^(th) section immediately after shutting thewellbore in,

.

For quantitative estimations of both effects, it is necessary to know adependency of the downhole fluid temperature upon the depth at differenttimes after shutting the wellbore in. Transient (non-stationary)profiles of the downhole temperature should be measured during thewellbore testing or obtained as a result of the numerical or analyticalsimulation.

We propose to calculate a corrected downhole pressure value (from whichthe influence of the fluid density and tubing length variation isexcluded) by a formula (4):

P _(g) _(—) _(r)(t)=P _(g)(t)+ΔP(t),  (4)

where P_(g) (t) is a measured pressure, Pa, ΔP(t) is a correction takingan influence of temperature effects into account and being calculated bythe formulae (1)-(3).

In case of high-productive formations, a pressure in a shut-in wellrapidly increases up to short of an initial pressure. Hereupon, there isa long and slow increase in the pressure, and the temperature effectsconsidered above can have an essential influence upon the dynamics ofsaid increase. In some cases, the measured pressure can decrease intime.

FIG. 1 shows a comparison of the bottom hole pressure recovery dynamicsduring the wellbore shut-in under isothermal and non-isothermalconditions. The pressure recovery dynamics in an oil formation afterproduction of oil at a flow rate of 2,000 m³/day for 20 hours isillustrated by a dashed line (Isothermal). This dependency was obtainedby the Saphir module in the program Ecrin v4.30 using the option “TestDesign” for a uniform formation having a length of 100 m, a permeabilityof 2 d at a well skin of 5 and an outer formation radius of 1,500 M. Itwas supposed that the temperature is constant in the formation and inthe well.

A solid line (Non-isothermal) shows calculation results for the samewellbore testing but with taking the non-isothermal effects intoaccount. It was supposed that the pressure sensor is on the tubing at adepth of 100 m above the upper boundary of the reservoir. According tothe calculation, an average temperature of a fluid filling the tubinghas been decreased by 37° C. during the pressure recovery, while adensity of a fluid in the wellbore has been increased by 10 kg/m³.

The decrease in the average temperature of the downhole fluid in theshut-in wellbore in the present case is 37° C. The processing of thepressure curve (Non-isothermal) resulted from measurement by standardisothermal techniques in the shut-in wellbore at such a pressure changegives an incorrect formation model, its permeability and a well skinfactor.

Thus, to exclude the influence of the thermal effects, it is necessaryto correct the results of measuring the downhole pressure.

The possibility to correct the measured pressure using the method of thedisclosure is shown by synthetic examples prepared using the numericalsimulator T-Mix (Ramazanov, A. Sh., et al. Termogidravlicheskieissledovania v skvazhine dlya opredelenia parametrov priskvazhinnoi zonyplasta i debitov mnogoplastovoi sistemy” (Thermohydrodynamic Studies InWell For Determining Parameters Of Formation Nearfield and MultilayeredSystem Flow Rates), 2010, SPE 136256). It is a code allowing simulationof transient pressure and temperature distributions when a single-phasefluid flows in a formation and in a wellbore, said code being able toreproduce an arbitrary sequence of production operations in thewellbore: the production beginning, the flow rate variation, thewellbore shutting in, etc.

The transient pressure distribution in the formation is simulated usingthe Darcy filtration law for a cylindrical gas flow or apoorly-compressible liquid in a layered medium. The downhole pressure iscalculated using the quasi-stationary law of conservation of momentumwith taking into account a friction force, a gravity force, anacceleration, and an effect of a wellbore filled with a compressiblefluid.

The transient formation temperature field is calculated taking intoaccount the conductive and convective heat transfer, the adiabaticeffect, and the Joule-Thomson effect. The transient thermal model of thewellbore takes into account the fluid mixing effect, the heat exchangebetween the well and surrounding rocks as well as the adiabatic effectand the fluid heating due to viscous friction forces.

According to the method described above, a transient temperaturedistribution along the wellbore is measured or simulated; adequacy ofthe simulation is controlled by matching of simulated transientpressure, temperature and flow rate with available measurement resultsof said quantities for the whole testing duration.

The temperature, the pressure, and the flow rate were calculated forvalues of parameters of the wellbore, the reservoir and the sequence ofoperations described above, using the numerical simulator T-Mix.

The simulation had the following parameters:

properties of the reservoir: homogeneous, the reservoir thickness—100 m;the initial reservoir pressure at the outer boundary of the radius of1500 m was fixed to be 7,251.89 psi; the reservoir permeability—2 d; thetemperature—120° C.; the well skin—5; the wellbore depth—4,000 m;

properties of the fluid: oil having the density of 800 kg/m³ underformation conditions, thermal conductivity of 0.14 W/m/K, specific heatcapacity of 2000 J/kg/K, viscosity of 1 cP, compressibility of 6.9×10⁻⁶psi⁻¹.

The sequence of production operations in the wellbore is as follows:circulation for 70 hrs; shut-in for 70 hrs; production at the flow rateof 2,000 M³ per day for 20 hrs (70 to 90 hrs, FIG. 2, 3); shut-in for 30hrs (90 to 120 hrs, FIG. 2, 3).

FIG. 2 shows the results of simulating the fluid temperature at theupper formation boundary (TOR), at the sensor depth (100 m above theformation) and at the surface. FIG. 3 shows the results of calculatingthe downhole pressure at the sensor depth (100 m above the formation).The calculation was carried out using the numerical simulator T-Mixthrough the wellbore testing time.

The second step is to obtain the transient downhole temperature profileswhen the wellbore is shut in, said profiled being derived from numericalcalculations using a model having input parameters that give the bestmatch with available measurements. FIG. 4 shows the results ofsimulating the non-stationary temperature profiles along the wellborefor the wellbore shut-in mode used to process the GDS results (90 to 120hrs).

The resulted transient (non-stationary) temperature profiles are used tocalculate change in the downhole fluid density and the tubing lengthwhen the wellbore is shut in. The distance between the tubing anchoragepoint and the pressure sensor was divided into 78 equal sections. Theaverage downhole fluid temperature change in time,

${{\Delta \; T_{t}} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}( {T_{oi} - {T_{i}(t)}} )}}},$

between the tubing anchorage point and the pressure sensor, the downholefluid density variation between the sensor and the upper boundary of thereservoir, and the tubing length reduction in the shut-in wellbore werecalculated by the formulae (2)

(3). The results of simulating the wellbore shut-in mode for 90 to 120hr are shown in FIGS. 5 a, 5 b, and 5 c. The reduction in the averagetemperature of downhole fluid in the shut-in well was 37° C. in thiscase. The downhole fluid density between the pressure sensor and theformation has decreased by 10 kg/m³ for the value α_(f)=1.5·10⁻³ K⁻¹ ofthe volumetric thermal expansion coefficient of the fluid. At the sametime, the tubing length has reduced by 1.7 m for the value α_(t)=12·10⁻⁶K⁻¹ of the linear thermal expansion coefficient of the tubing.

The final step is correction of the downhole pressure measurementresults by the formula (4) taking into account the obtained results withrespect to the downhole fluid density and the tubing length in order toexclude the influence of non-isothermal effects. FIG. 6 shows thepressure recovery dynamics in the oil formation after production, saiddynamics corresponding to readings of the sensor arranged at 100 m abovethen upper formation boundary (the solid curve), and the calculationresults for the same well study but with taking the influence ofnon-isothermal effects (the dashed curve).

1. A method for determining a downhole pressure, comprising: measuringthe pressure in the wellbore during the wellbore testing; measuring atemperature at least at one point of the wellbore during the wellboretesting; determining transient profiles of the temperature along thewellbore during the wellbore testing; calculating changes in a densityof a downhole fluid and in a length of a tubing when the wellbore isshut in; and correcting the pressure measurement results on the basis ofthe calculated changes in the density of the downhole fluid and in thelength of the tubing.
 2. The method of claim 1, wherein the transientprofiles of the temperature along the wellbore are determined bymeasuring the temperature along the wellbore using a system of sensorsdistributed on the wellbore at different depths.
 3. The method of claim2, wherein the transient profiles of the temperature along the wellboreare obtained by interpolating the measured temperatures.
 4. The methodof claim 1, wherein the transient profiles of the temperature along thewellbore are determined by numerical or analytical simulating thetemperature profile.
 5. The method of claim 1, wherein the pressure ismeasured by at least one sensor disposed at a fixed depth within thewellbore.